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Queueing with redundant requests: exact analysis

Author

Listed:
  • Kristen Gardner

    (Carnegie Mellon University)

  • Samuel Zbarsky

    (Carnegie Mellon University)

  • Sherwin Doroudi

    (Carnegie Mellon University)

  • Mor Harchol-Balter

    (Carnegie Mellon University)

  • Esa Hyytiä

    (University of Iceland)

  • Alan Scheller-Wolf

    (Carnegie Mellon University)

Abstract

Recent computer systems research has proposed using redundant requests to reduce latency. The idea is to run a request on multiple servers and wait for the first completion (discarding all remaining copies of the request). However, there is no exact analysis of systems with redundancy. This paper presents the first exact analysis of systems with redundancy. We allow for any number of classes of redundant requests, any number of classes of non-redundant requests, any degree of redundancy, and any number of heterogeneous servers. In all cases we derive the limiting distribution of the state of the system. In small (two or three server) systems, we derive simple forms for the distribution of response time of both the redundant classes and non-redundant classes, and we quantify the “gain” to redundant classes and “pain” to non-redundant classes caused by redundancy. We find some surprising results. First, the response time of a fully redundant class follows a simple exponential distribution and that of the non-redundant class follows a generalized hyperexponential. Second, fully redundant classes are “immune” to any pain caused by other classes becoming redundant. We also compare redundancy with other approaches for reducing latency, such as optimal probabilistic splitting of a class among servers (Opt-Split) and join-the-shortest-queue (JSQ) routing of a class. We find that, in many cases, redundancy outperforms JSQ and Opt-Split with respect to overall response time, making it an attractive solution.

Suggested Citation

  • Kristen Gardner & Samuel Zbarsky & Sherwin Doroudi & Mor Harchol-Balter & Esa Hyytiä & Alan Scheller-Wolf, 2016. "Queueing with redundant requests: exact analysis," Queueing Systems: Theory and Applications, Springer, vol. 83(3), pages 227-259, August.
    • Handle: RePEc:spr:queues:v:83:y:2016:i:3:d:10.1007_s11134-016-9485-y
    DOI: 10.1007/s11134-016-9485-y
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    Citations

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    Cited by:

    1. Céline Comte & Jan-Pieter Dorsman, 2021. "Pass-and-swap queues," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 275-331, August.
    2. Gideon Weiss, 2022. "Parallel multi-type many server conjecture," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 269-271, April.
    3. Zhao, Chen & Wang, Zhongbin, 2023. "The impact of line-sitting on a two-server queueing system," European Journal of Operational Research, Elsevier, vol. 308(2), pages 782-800.
    4. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
    5. Francisco Castro & Hamid Nazerzadeh & Chiwei Yan, 2020. "Matching queues with reneging: a product form solution," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 359-385, December.
    6. Gideon Weiss, 2020. "Directed FCFS infinite bipartite matching," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 387-418, December.
    7. Kristen Gardner & Rhonda Righter, 2022. "The cost of collaboration," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 7-40, February.
    8. Leela Nageswaran, 2023. "Implications of vaccine shopping during pandemic," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1133-1149, April.
    9. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    10. Youri Raaijmakers & Sem Borst & Onno Boxma, 2019. "Redundancy scheduling with scaled Bernoulli service requirements," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 67-82, October.
    11. Kristen Gardner & Rhonda Righter, 2020. "Product forms for FCFS queueing models with arbitrary server-job compatibilities: an overview," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 3-51, October.

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